I'm not sure I buy this one, at least not without seeing some elaboration. It seems that the "privileged viewpoint" card being played here is irrelevant to the particular kind of mediocrity relevant to the argument. Carter's maths apply whether or not the population is aware of it. We're interested only in the area under the curve, not which bit of that curve is self-aware.
A bunch of superintelligent aliens roaming the galaxy might stop at a mediaeval planet and say: "There's a 95% chance they'll all be dead before x more births." Then they see us, and say "There's a 95% chance they'll all be dead before y more births. Then they move on to a star-spanning civilization that has been aware of Carter's calculation for many millennia: "There's a 95% chance they'll all be dead before z more births." If Carter's maths apply, 5% of such predictions will be wrong, the other 95% will be correct.

Grant Hutchison

Edit:If anything, Hanson's suggestion serves to undermine one of the counterarguments to Carter: that external evidence indicates species survive for many more million years than we have done so far, so we are more likely to be at the start of our career as a species. But our privileged viewpoint as a self-aware, mathematical, industrial civilization means that we are not like other species, and so their data cannot be applied to us.